## #1176 Spurious solutions (zero denominators) returned by solve

open
nobody
5
2007-06-29
2007-04-26
Anonymous
No

I was trying to calculate the equation of a hyperbola of the type x^2/a^2 - y^2/b^2 = 1, given two points. Maxima finds, among others, also a wrong solution [a=0,b=0].

(%i4) hyp:x^2/a^2-y^2/b^2=1\$
(%i4) eq1:hyp,x=-5/2,y=-3/4\$
(%i4) eq2:hyp,x=10/3,y=4/3\$
(%i4) solve([eq1,eq2],[a,b]);
(%o4) [[a=2,b=-1],[a=-2,b=-1],[a=2,b=1],[a=-2,b=1],[a=0,b=0]]

F. Buratti (Italy)
bufranz@hotmail.com

Maxima version: 5.11.99rc2
Maxima build date: 20:46 4/19/2007
host type: i686-pc-mingw32
lisp-implementation-type: GNU Common Lisp (GCL)
lisp-implementation-version: GCL 2.6.8

## Discussion

• Stavros Macrakis - 2007-05-01

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user_id=588346
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Yes, this is a bug. Here is a simpler example:

solve([1/a-1/b=1,a=b],[a,b]) => [[a=0,b=0]]

• Stavros Macrakis - 2007-05-01
• labels: --> Lisp Core - Solving equations

• Robert Dodier - 2007-06-29
• summary: Wrong solution of system --> Spurious solutions (zero denominators) returned by solve

• Robert Dodier - 2007-06-29

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user_id=501686
Originator: NO

Merging bug report # 1700056 (same problem); I'll mark 1700056 as a dup. Also revise summary to make it more descriptive.

------------- begin 1700056 -------------
With Maxima 5.11.0, Using Lisp CLISP 2.41 (2006-10-13)

q1 : 2/x + 5/y = -19/15;
q2 : 1/y -5/x = -4/3;
sys :[q1,q2];
var : [x,y];
solve(sys,var);
/*==> [[x = 5,y = -3],[x = 0,y = 0]]

This seems to happen only with systems. I was not able
to reproduce this bug with a single equation and a single
variable.
-------------- end 1700056 --------------